2023/04/27 by Wagner, Stefan
#46L87 (primary) #55R10 (secondary) #58B34 #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Operator Algebras (math.OA)
paper · doi:10.48550/arxiv.2304.14010
We apply ourselves to the noncommutative geometry of frame bundles by showing that each C^*-algebraic noncommutative principal SO(n)-bundle is, up to isomorphism, uniquely determined by its associated noncommutative vector bundle with respect to the standard representation of SO(n). For this, we provide a construction procedure, via unitary tensor functors, that for a certain type of correspondence, let's say M, attaches a free C^*-dynamical system (AM,SO(n),αM) with the property that its associated noncommutative vector bundle with respect to the standard representation of SO(n) is isomorphic to M.